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As regulators pay more attentions to losses rather than gains, we are able to derive a new class of risk statistics, named regulator-based risk statistics with scenario analysis in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou et al. \cite{11}, and also data-based versions of loss-based risk measures introduced by Cont et al. \cite{5} and Sun et al. \cite{12}.

Assessing the demand hazards of structures is requested in the framework of performance-based earthquake engineering. An efficient method for estimating the seismic risk of structures is proposed in this paper. The relationship between multiple limit capacities and corresponding response parameters is denoted by using a generalized multidimensional limit state equation. The limit states of different components are described as random and convex mixed variables. The seismic responses of different components are considered dependent and follow a multidimensional lognormal distribution. The mathematical formula of multidimensional demand hazards of structures is then derived through combining the seismic fragility function and the seismic hazard curve. The proposed method is used to perform the demand hazard analysis and the parameter sensitivity analysis of a multispan continuous concrete girder bridge, selecting column ductility and bearing displacement as the two-dimensional seismic response parameters obtained by Incremental Dynamic Analysis. The results demonstrate that the coefficient of variation and correlation coefficient N, which are involved in the limit state equation, have an impact on the evaluation of the demand hazards.

In low SNR condition, it is difficult to identify the radio transient characteristics of the signals. To solve this problem, a new recognition algorithm based on multifractal dimension characteristics is proposed. In fractal theory, multifractal dimension is the most sophisticated characterize that can describe the similar characteristics of the signals. Therefore, multifractal dimension is used in this paper to extract the subtle features of different impulse noise signals, in order to achieve the purpose of the classification and identification of the radiation source.

New technologies are advancing and emerging day by day to improve the safety of humans by making use of various autonomous technologies. The continuous utilization of autonomous vehicles/systems in search and rescue (SAR) operations is a challenging research area particularly for marine-based activities. A comprehensive systematic literature review (SLR) providing an overview of improvisations that have been done in the field of autonomous technologies for search and rescue operation over the last five years has been compiled in this paper. A methodology for using autonomous vehicles in water for SAR operations has been incorporated and demonstrated. The focus of this study is to look at the various techniques and address different challenges faced for human beings’ safety during rescue operation. The comparison of results achieved for various technologies and algorithms is highlighted in this paper. This literature survey proves to be a good source of information for fellow researchers to precisely analyze the study results.

Homomorphic aggregate signature (HAS) is a linearly homomorphic signature (LHS) for multiple users, which can be applied for a variety of purposes, such as multi-source network coding and sensor data aggregation. In order to design an efficient postquantum secure HAS scheme, we borrow the idea of the lattice-based LHS scheme over binary field in the single-user case, and develop it into a new lattice-based HAS scheme in this paper. The security of the proposed scheme is proved by showing a reduction to the single-user case and the signature length remains invariant. Compared with the existing lattice-based homomorphic aggregate signature scheme, our new scheme enjoys shorter signature length and high efficiency.

A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.

We consider the design of fixed-order (or low-order) linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,𝒬-stabilization as a robust stabilization problem, and robustL∞control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI) of the typeBGC+(BGC)T+Q<0for the unknown matrixG. Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured) positive definite matrixXsuch thatX∈𝒞1andX−1∈𝒞2where𝒞1and𝒞2are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

International audience; This paper concerns the problem of stabilizing linear time-delay systems under state and control linear constraints. For this, necessary and sufficient conditions for a given polyhedral set (possibly non-symmetrical) to be positively invariant are obtained. The existence conditions of linear state feedback control laws respecting the constraints are established, and a procedure is given in order to compute such a controller. The paper presents memoryless controlled systems but the results can be applied to cases of delayed-controlled systems. An example is given.

In this paper we consider optimal control problem for infinite dimensional uncertain systems. Necessary conditions of optimality are presented under the assumption that the principal operator is the infinitesimal generator of a strongly continuous semigroup of linear operators in a reflexive Banach space. Further, a computational algorithm suitable for computing the optimal policies is also given.

In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane) inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate). On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells) by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.

In this paper a survey of the most effective methods in singular perturbations is presented. Many applied problems can be modeled by nonlinear singularly perturbed systems, as, for example, problems in kinetics, biochemistry, semiconductors theory, theory of electrical chains, economics, and so on. In this survey we consider averaging and constructive methods that are very useful from the point of view of their numerical and computer realizations.

This paper considers the problem of assigning the dynamics of a nonlinear analytic system using nonlinear generalized sampled-data hold function (GSHF) control, in the neighborhood of an equilibrium point. On every sampling interval, the control input consists of a nonlinear time-periodic function applied to the sampled value of the state vector. The nonlinear monodromy map is the state transition map from one sample time to the next. It is shown that this map is arbitrarily assignable by GSHF feedback if and only if the linear part of the system is controllable. Two approaches are proposed to construct a GSHF controller that performs the assignment. The first approach matches the coefficients of the Taylor series expansion of the monodromy map around the equilibrium. The second approach interpolates an optimal control law at several points in the vicinity of the equilibrium. These approaches are illustrated on an example.

In this paper we provide sufficient conditions for the existence and uniqueness of the solution of the newly obtained equation of motion for constrained mechanical systems.

In this paper, a periodic finite-span beam subjected to the stochastic acoustic pressure with bounded parameters is investigated. Uncertainty parameters exist in this acoustic excitation due to the deviation or imperfection. First, a finite-span beams subjected to the random acoustic pressure field are studied, the exact analytic forms of the cross-spectral density of both the transverse displacement and the bending moment responses of the structure are formulated. The combined probabilistic and convex modeling of acoustic excitation appears to be most suitable, since there is an insufficient information available on the acoustic excitation parameters, to justify the totally probabilitic analysis. Specifically, we postulate that the uncertainty parameters in the acoustic loading belong to a bounded, convex set. In the special case when this convex set is an ellipsoid, closed form solutions are obtained for the most and least favorable mean square responses of both the transverse displacement and bending moment of the structure. Several finite-span beams are exemplified to gain insight into proposal methodology.

The asymptotic behavior as λ → ∞ of the function U ( x , λ ) that satisfies the reduced wave equation L λ [ U ] = ∇ ⋅ ( E ( x ) ∇ U ) + λ 2 N 2 ( x ) U = 0 on an infinite 3-dimensional region, a Dirichlet condition on ∂ V , and an outgoing radiation condition is investigated. A function U N ( x , λ ) is constructed that is a global approximate solution as λ → ∞ of the problem satisfied by U ( x , λ ) . An estimate for W N ( x , λ ) = U ( x , λ ) − U N ( x , λ ) on V is obtained, which implies that U N ( x , λ ) is a uniform asymptotic approximation of U ( x , λ ) as λ → ∞ , with an error that tends to zero as rapidly as λ − N ( N = 1 , 2 , 3 , ... ) . This is done by applying a priori estimates of the function W N ( x , λ ) in terms of its boundary values, and the L 2 norm of r L λ [ W N ( x , λ ) ] on V . It is assumed that E ( x ) , N ( x ) , ∂ V and the boundary data are smooth, that E ( x ) − I and N ( x ) − 1 tend to zero algebraically fast as r → ∞ , and finally that E ( x ) and N ( x ) are slowly varying; ∂ V may be finite or infinite. The solution U ( x , λ ) can be interpreted as a scalar potential of a high frequency acoustic or electromagnetic field radiating from the boundary of an impenetrable object of general shape. The energy of the field propagates through an inhomogeneous, anisotropic medium; the rays along which it propagates may form caustics. The approximate solution (potential) derived in this paper is defined on and in a neighborhood of any such caustic, and can be used to connect local “geometrical optics” type approximate solutions that hold on caustic free subsets of V .The result of this paper generalizes previous work of Bloom and Kazarinoff [C. O. BLOOM and N. D. KAZARINOFF, Short Wave Radiation Problems in Inhomogeneous Media: Asymptotic Solutions, SPRINGER VERLAG, NEW YORK, NY, 1976].

Linear, constant-coefficient difference equations play a central role in many areas of engineering, where cases involving repeated zero-valued characteristic roots are sometimes of particular interest. Unfortunately, the classical solution expression presented in the mathematical literature of difference equations is not valid for this latter case. In this paper we develop a unique generalization of the classical solution expression for linear, constant-coefficient, homogeneous difference equations that accommodates the most general case of repeated zero-valued characteristic roots, thereby “completing” the classical theory. A worked example is presented to illustrate our result.

An analytical framework for analysis of a class of nonlinear systems with time varying inputs is presented. It is shown that the trajectories of the transformed nonlinear systems are uniformly bounded with an ultimate bound under certain conditions shown in this paper. The result obtained is useful for applications, in particular, analysis and design of gain scheduling.

This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.

This paper deals with the robustness of the class of nonlinear piecewise deterministic systems with unknown but bounded uncertainties. Under the assumption that all the modes of the markovian jump process (disturbance) communicate, the complete access to the system state and the boundedness of the uncertainties, a sufficient condition for stochastic stability of this class of systems is given. An example is presented to validate the proposed results.

A large class of emerging actuation devices and materials exhibit strong hysteresis characteristics during their routine operation. For example, when piezoceramic actuators are operated under the influence of strong electric fields, it is known that the resulting input–output behavior is hysteretic. Likewise, when shape memory alloys are resistively heated to induce phase transformations, the input–output response at the structural level is also known to be strongly hysteretic. This paper investigates the mathematical issues that arise in identifying a class of hysteresis operators that have been employed for modeling both piezoceramic actuation and shape memory alloy actuation. Specifically, the identification of a class of distributed hysteresis operators that arise in the control influence operator of a class of second order evolution equations is investigated. In Part I of this paper we introduce distributed,hysteretic control influence operators derived from smoothed Preisach operators and generalized hysteresis operators derived from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hysteretic control influence operator can be expressed as an ouput least square minimization over probability measures defined on a compact subset of a closed half-plane. In Part II of this paper, consistent and convergent approximation methods for identification of the measure characterizing the hysteresis are derived.

In this paper we consider Lagrange type control problem for systems involving dynamic boundary conditions that is, with boundary operators containing time derivatives. Assuming the existence of optimal controls,B-evolutions theory is used to present necessary conditions of optimality. The result is illustrated by an example from heat transfer problem and also an algorithm for computing optimal controls is presented.

The main purpose of this paper is to incorporate a refined hysteresis model, viz. a vector Preisach model, in 2D magnetic field computations. To this end the governing Maxwell equations are rewritten in a suitable way, which allows to take into account the proper magnetic material parameters and, moreover, to pass to a variational formulation. The variational problem is solved numerically by a FE approximation, using a quadratic mesh, followed by the time discretisation based upon a modified Cranck Nicholson algorithm. The latter includes a suitable iteration procedure to deal with the nonlinear hysteresis behaviour. Finally, the effectiveness of the presented mathematical tool has been confirmed by several numerical experiments.

The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

An approach to the optimum design of structures, in which uncertainties with a fuzzy nature in the magnitude of the loads are considered, is proposed in this study. The optimization process under fuzzy loads is transformed into a fuzzy optimization problem based on the notion of Werners' maximizing set by defining membership functions of the objective function and constraints. In this paper, Werner's maximizing set is defined using the results obtained by first conducting an optimization through anti-optimization modeling of the uncertain loads. An example of a ten-bar truss is used to illustrate the present optimization process. The results are compared with those yielded by other optimization methods.

This paper deals with the robustness of the class of uncertain linear systems with Markovian jumping parameters (ULSMJP). The uncertainty is taken to be time-varying norm bounded. Under the assumptions of the boundedness of the uncertainties and the complete access to the system's state and its modes, a sufficient condition for stochastic stabilizability of this class of systems is established. An example is provided to demonstrate the usefulness of the proposed theoretical results.

This paper considers the characterization and computation of invariant sets for discrete-time, time-invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance-invariant sets X that belong to a specified subset Γ of the state space. Such d-invariant sets have important applications in control problems where there are pointwise-in-time state constraints of the form χ ( t ) ∈ Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.

In Ref. [6] the authors constructed analytical solutions including one arbitrary function for the problem of nonlinear, unsteady, supersonic flow analysis concerning slender bodies of revolution due to small amplitude oscillations. An application describing a flow past a right circular cone was presented and the constructed solutions were given in the form of infinite series through a set of convenient boundary and initial conditions in accordance with the physical problem. In the present paper we develop an appropriate convergence analysis concerning the before mentioned series solutions for the specific geometry of a rigid right circular cone. We succeed in estimating the limiting values of the series producing velocity and acceleration resultants of the problem under consideration. Several graphics for the velocity and acceleration flow fields are presented. We must underline here that the proposed convergence technique is unique and can be applied to any other geometry of the considered body of revolution.

A numerical method for solving linear quadratic optimal control problems with control inequality constraints is presented in this paper. The method is based upon hybrid function approximations. The properties of hybrid functions which are the combinations of block-pulse functions and Legendre polynomials are first presented. The operational matrix of integration is then utilized to reduce the optimal control problem to a set of simultaneous nonlinear equations. The inequality constraints are first converted to a system of algebraic equalities, these equalities are then collocated at Legendre–Gauss–Lobatto nodes. An illustrative example is included to demonstrate the validity and applicability of the technique.

The problems of robust performance and feedback control synthesis for a class of linear discrete-time systems with time-varying parametric uncertainties are addressed in this paper. The uncertainties are bound and have a linear matrix fractional form. Based on the concept of strongly robust H∞-performance criterion, results of robust stability and performance are developed and expressed in easily computable linear matrix inequalities. Synthesis of robust feedback controllers is carried out for several system models of interest.

In this paper a simple introduction to the problem of the regularization of ill-posed problems (IPP) is presented. We describe three regularization methods with simple examples which illustrate the principle that for “bad” equations it is unprofitable to carry out exact computations.

In this paper, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.

For a connected graph J, a subset W ⊆ V J is termed as a locating-total dominating set if for a ∈ V J , N a ∩ W ≠ ϕ , and for a , b ∈ V J − W , N a ∩ W ≠ N b ∩ W . The number of elements in a smallest such subset is termed as the locating-total domination number of J. In this paper, the locating-total domination number of unicyclic graphs and bicyclic graphs are studied and their bounds are presented. Then, by using these bounds, an upper bound for cacti graphs in terms of their order and number of cycles is estimated. Moreover, the exact values of this domination variant for some families of cacti graphs including tadpole graphs and rooted products are also determined.

In this paper, we address the analysis and the state-feedback synthesis problems for linear parameter-varying (LPV) sampled-data control systems. We assume that the state-space data of the plant and the sampling interval depend on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. We explore criteria such as the stability, the energy-to-energy gain (inducedL2norm) and the energy-to-peak gain (inducedL2-to-L∞norm) of such sampled-data LPV systems using parameter-dependent Lyapunov functions. Based on these analysis results, the sampled-data state-feedback control synthesis problems are examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities that can be solved via efficient interior-point algorithms.

This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with annth order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of thenth order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal.24(1), 1973) are a particular case.

In this paper, we consider fluid queue models with infinite buffer capacity which receives and releases fluid at variable rates in such a way that the net input rate of fluid into the buffer (which is negative when fluid is flowing out of the buffer) is uniquely determined by the number of customers in anM/M/1/Nqueue model (that is, the fluid queue is driven by this Markovian queue) with constant arrival and service rates. We use some interesting identities of tridiagonal determinants to find analytically the eigenvalues of the underlying tridiagonal matrix and hence the distribution function of the buffer occupancy. For specific cases, we verify the results available in the literature.

This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI). The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable.We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.

This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assuresH2guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

In this paper we consider the Finite Signal-to-Noise ratio model for linear stochastic systems. It is assumed that the intensity of noise corrupting a signal is proportional to the variance of the signal. Hence, the signal-to-noise ratio of each sensor and actuator is finite – as opposed to the infinite signal-to-noise ratio assumed in LQG theory. Computational errors in the controller implementation are treated similarly. The objective is to design a state feedback control law such that the closed loop system is mean square asymptotically stable and the output variance is minimized. The main result is a controller which achieves its maximal accuracy with finite control gains – as opposed to the infinite controls required to achieve maximal accuracy in LQG controllers. Necessary and sufficient conditions for optimality are derived. An optimal control law which involves the positive definite solution of a Riccati-like equation is derived. An algorithm for solving the Riccati-like equation is given and its convergence is guaranteed if a solution exists.

The contribution of this paper is twofold. First we give a generalization of theS-procedure which has been proven useful for robustness analysis of control systems. We then apply the generalizedS-procedure to derive an extension of the Kalman – Yakubovich – Popov lemma that converts a frequency domain condition within a finite interval to a linear matrix inequality condition suitable for numerical computations.

In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.

This paper outlines a methodology to study the stability of Takagi-Sugeno's (TS) fuzzy models. The stability analysis of the TS model is performed using a quadratic Liapunov candidate function. This paper proposes a relaxation of Tanaka's stability condition: unlike related works, the equations to be solved are not Liapunov equations for each rule matrix, but a convex combination of them. The coefficients of this sums depend on the membership functions. This method is applied to the design of continuous controllers for the TS model. Three different control structures are investigated, among which the Parallel Distributed Compensation (PDC). An application to the inverted pendulum is proposed here.

The object of investigation in this paper is a nonlinear ordinary differential equation obtained by means of self-similar reduction of the generalized Burgers equation $u_t+u^\beta u_x+\lambda u^\alpha=\delta u_{xx}$ with the nonlinear damping term $\lambda u^\alpha$. More exactly, the authors study the initial value problem $g"+2\eta g'+2\beta^{-1}g-2^{3/2}g^\beta g'-4\lambda g^\alpha=0$, $g(0)=\nu$, $g'(0)=0$ by using both numerical and analytical methods. Here $\alpha>0$, $\beta=(\alpha-1)/2>0$, $\lambda$, $\delta>0$ and $\nu >0$ are constants. Existence of positive bounded solutions with exponential and algebraic types of decay to zero at infinity is proved for special ranges of parameters.

In this paper we develop a unified dynamical systems framework for a general class of systems possessing left-continuous flows; that is, left-continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid, impulsive, and switching dynamical systems as special cases. Furthermore, we generalize dissipativity, passivity, and nonexpansivity theory to left-continuous dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to left-continuous dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time dynamics, and dissipated energy over the resetting events. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left-continuous dynamical systems. These results generalize the positivity and small gain theorems to the case of left-continuous, hybrid, and impulsive dynamical systems.

In a previous paper, we discussed the characteristics of a “meaningful” average of a collection of dynamical systems, and introduced as well as contructed a “meaningful” average that is not usually what is meant by an “ensemble” average. We also addressed the associated issue of the existence and construction of such an average for a class of interconnected, linear, time invariant dynamical systems. In this paper, we consider the issue of the construction of a meaningful average for a collection of a class of nonlinear dynamical systems. The construction of the meaningful average will involve integrating a nonlinear differential equation, of the same order as that of any member of the systems in the collection. Such an “average” dynamical system is not only attractive from a computational perspective, but also represents the macroscopic behavior of the interconnected dynamical systems. An average dynamical system can be used in the analysis and design of hierarchical systems.

In this paper, we investigate the problems of robust stability and ℋ∞-estimation for a class of linear discrete-time systems with time-varying norm-bounded parameter uncertainty and unknown state-delay. We provide complete results for robust stability with prescribed performance measure and establish a version of the discrete Bounded Real Lemma. Then, we design a linear estimator such that the estimation error dynamics is robustly stable with a guaranteed ℋ∞-performance irrespective of the parameteric uncertainties and unknown state delays. A numerical example is worked out to illustrate the developed theory.

In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.

In this paper, we investigate the robust passivity analysis and synthesis problems for a class of uncertain time-delay systems. This class of systems arises in the modelling effort of studying water quality constituents in fresh stream. For the analysis problem, we derive a sufficient condition for which the uncertain time-delay system is robustly stable and strictly passive for all admissible uncertainties. The condition is given in terms of a linear matrix inequality. Both the delay-independent and delay-dependent cases are considered. For the synthesis problem, we propose an observer-based design method which guarantees that the closed-loop uncertain time-delay system is stable and strictly passive for all admissible uncertainties. Several examples are worked out to illustrate the developed theory.

In the present paper Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Gaursat's functions for the first and second fundamental problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped on the domain outside a unit circle by means of general rational mapping function. Some applications are investigated. The interesting cases when the shape of the hole takes different shapes are included as special cases.

The paper shows how to compute a diffeomorphic state space transformation in order to put the initial mutivariable nonlinear model into an appropriate regular form . This form is an extension of the one proposed by Lukyanov and Utkin [9], and constitutes a guidance for a “natural” choice of the sliding surface. Then stabilization is achieved via a sliding mode strategy. In order to overcome the chattering phenomenon, a new nonlinear gain is introduced.

In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operatorB, conditions under which operatorBcan be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllabilityN(μ). Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operatorN(μ)in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.